In this paper, the authors propose a distributed rate allocation algorithm for delay minimal data delivery in overlay networks where multiple sources compete simultaneously for the available network resources. In order to efficiently utilize the network resources, they propose to use inter-session network coding. They devise a distributed algorithm that allows peers to determine the optimal coding combinations and the packet rates for each type of combinations to be requested from the parent peers. The rate allocation problem is formulated as a decoding delay minimization problem, where every peer seeks the rates that minimize the average expected delay of the peer and its children peers.